German 6th Standard Resolution
German 6th Full Resolution
Jazz Minor Cadence
Swiss 6th Resolution
Inverse Commontone Diminished
French 6th Resolution
Tristan 6th Full Resolution
Tristan 6th to Dominant
Tristan Half Cadence
Augmented-Minor 7th Resolution
Major-Diminished 7th Resolution
Minor-Augmented 6th Resolution
Eulenspiegel 6th Resolution
Belgian 6th to Tonic
Sweet Adeline Chords
Five Chord Scissor
With the discovery of the Web Audio API, using in particular the oscillator node found in all the major browsers, I was inspired to dig up this older idea of mine to play the component chords of a progression by moving the mouse over glass buttons. The following are some four-part chord progressions. Move the mouse over the button lights to hear the chords in Pythagorean tuning. The notes are played based on the note names (letter and accidental). Hold Shift while mousing to hear the chords in just intonation. This uses the frequency ratios provided by the parenthesized numbers. A chord sequence lists each chord's notes root, with its corresponding harmonic, and its four notes, with their corresponding harmonics. You can hear the chords in a progression by holding the mouse over each button to hear a chord. A different color is assigned to each chord in the sequence. The harmonic values of the notes are the ratio of frequency of each chord note to that of the root. The root's harmonic is its ratio of frequency of that note to a tonic of C. Conveniently, any frequency that is power of 2 (which by the way includes 1 hert) is a slighly flat C.
When examining harmonic values, it is bound to be a common source of confusion that the major 3rd of a chord is on the 5th harmonic and its 5th is on the 3rd harmonic. This is why it is good to get used to how the first 5th occurs before the first 3rd in the harmonic series. This accounts for the use of the barbershop tuning chord CGCE rather than CEGC.
V7 I; V7 i
The simplest move in the circle of fifths, 5 to 1, giving the strongest sense of finality. An example of this is “Little Lize”, which alternates between the tonic and dominant.
Also known as: five and tonic
Inverse: Inverse Cadence
Tritone Complement: German 6th Full Resolution
I II7; i II7
This is a move between the tonic and a dominant 7th chord on the 2nd degree (this chord is also the one used as a “secondary dominant”, i.e. a five of five). This chord pair makes a nice Lydian sound. These chords are found in the G major scale as IV and V7. These two chords work well in either order, allowing for a good static harmony between these two chords. Some Examples of this chord pair are songs like Tonight, Slaughter on Tenth Avenue and Can You Read My Mind?.
Or if you go directly from tonic to two, but proceed back to tonic in a circle of 5ths (I->II7->V7->I), you have the descending circle of fifths from two, as heard in Coney Island Baby and the verse to Aura Lee.
The one caveat for Coney Island Baby is that there is a quick dominant on 6 that cadences to the V/V, however it is sufficiently short to be discounted for our purposes.
Inverse: Spanish Cadence
Tritone Complement: German 6th and Tonic
This is a tonic chord leading to a dominant 7th chord on the submediant.
At this point it can be said that it is appropriate to tune the a VI7 to the Pythagorean 6 (27/16) if it will continue as a chain of descending 5ths to the tonic. This would be the traditional “ragtime progression”, as exemplified nicely in Hello My Baby. But otherwise it is more logical to tune it to the 5-Limit 6 (5/3), such as if resolving to a minor supertonic (ii), which will probably be tuned 5-limit 10/9 anyway. This is a good rule to follow for the longer ragtime progressions that follow. So I have given both tuning options for each of these.
Tritone Complement: Sunny Chords
This is a tonic chord leading to a dominant 7th chord on the mediant. From here you can continue in descending circle of fifths from three (I->III7->VI7->II7->V7->I), as exemplified nicely in Five Foot Two.
Tritone Complement: Inchworm Chords
This is a move between the tonic and a dominant 7th chord on the leading tone. From here you can continue in a descending circle of fifths from 7 (I->VII7->III7->VI7->II7->V7->I), as exemplified nicely in Mr. Sandman.
Tritone Complement: Amen Cadence
Tritone Complement: One Seven
Known known as: four and tonic, plagal cadence or Norwegian 6th resolution.
Also called the plagal cadence. Named after its common use to close hymns.
This is a tonic followed by a dominant 7th on the minor 7th degree. The name is inspired by its prominant use in the tune Inchworm. The 7th chord on this degree could be a true dominant 7th, or as a German or Swiss 6th depending on where it resolves.
Tritone Complement: One Three
This is a tonic followed by a dominant 7th on the minor 3rd degree. The name is inspired by its prominant use in the tune Sunny. The 7th chord on this degree could be a true dominant 7th, as it is in Sunny where it resolves down a 5th, or as a German or Swiss 6th depending on where it resolves.
Tritone Complement: One Six
VI+6/5 i; VI+6/5 I
This is a German 6th chord resolving to a tonic 6/4. The German can be found as the 7th chord on the 4th degree of the Hungarian-minor scale, even though it doesn't sound like a root position, so it is usually interpreted as an augmented 6th chord on the 6th degree. It has a more passionate sound than the common-tone diminished. The origin of the name is considered uncertain, but it's proliferation in the music of German composers like Beethoven and Schubert are a likely cause of this term being coined. Also common in barbershop for giving goosebumps.
The “German 6th” resolving to a major tonic frequently spells the note on the minor 3rd degree as a raised 2nd, seeing that it resolves up to a major 3rd. In this case it is called a Swiss 6th or English 6th. This is considered viable since both chords are in the Swiss scale. But it must also be considered that a chord with a doubly-augmented 4th is considered hyper-chromatic.
Inverse: Tristan Half-Cadence
Tritone Complement: One Two
Also called a “mozart 5th”, due to it resulting in a parallel 5th. There are ways to invert the chord to avoid this by making it a parallel 4th. But the resulting resolution sounds like something of a guitar chord, having a 5th in the bass and a doubled root.
Tritone Complement: Cadence
Inverse: Tristan 6th Full Resolution
Here the dominant 7th rather than going to the tonic, goes to the submediant whose two common tones with the tonic resolve the dominant tritone.
Inverse: Leading Cadence
Tritone Complement: Swiss 6th Resolution
This is the regular resolution of the diminished and half-diminished leading 7th chords to tonic. The special case of resolving the Half-Diminised to a minor conforms to the jazz minor scale.
Inverse: Deceptive Cadence
Tritone Complement: Eulenspiegel 6th Resolution
This is so-named because it is simply a mirror image of an Authentic Cadence. It can be heard as a supertonic half-diminished to tonic, or as a subdominant minor-6th to tonic. The tonic chord can be major or minor.
Inverse: Authentic Cadence
Tritone Complement: Tristan 6th Full Resolution
Also known as: Alsatian 6th Resolution
This fully resolves the chromatic intervals, the doubly-augmented 4th, the augmented 6th and the augmented 4th, of the Swiss 6th chord. This is really the mirror image of the fully resolving Eulenspiegel resolution done by Strauss. This can be heard a few times in barbershop, such as at “prettiest gal” in the intro to Redhead.
Inverse: Eulenspiegel 6th Resolution
Tritone Complement: Deceptive Cadence
This chord is another enharmonic of the Dominant 7th that is an augmented 6th, with the additional quirk of a double-augmented 4th. It can be found in the Swiss scale which is the union of the notes in the Swiss 6th and its resolving mediant triad.
Gives a sweet sound to music going into the Romantic era. The preferred spelling is the one that spells the chromatic notes of the 7th chord so they are altered in the direction they will resolve. Consequently the spelling is related closely to the VII7 if resolving to a major tonic (CD#F#A-CEG) and to II7 if resolving to a minor tonic (CEbF#A-CEbG).
Based on the rule of resolving notes in the direction of alteration, the desired spelling for the CTD in the major key is GCEG -> ACD#F# (akin to the C->B7). And in the minor it should be GCEbG -> ACEbF# (akin to the Cm->D7). Both of these progressions can be found in the harmonic-minor. viio7->iv in the case of the minor triad and viio7->VI in the case of the major triad. That this still leaves some choice on the tuning matter is implied by the fact that a just barbershop 7th is still tuned as 4:5:6:7, whether the 7/5 interval is a diminished 5th (as in a dominant 7th) or an augmented 4th (as in a German 6th).
This is a colorful variant of the Commontone Diminished in which a barbershop 7th is substituted for the resolving triad. It is named after its use in the intro to Offenbach's Barcarolle. It is very commonly used in classical music, particularly in the romantic, and sticks tighly in your head after being heard in such works as Schubert’s 7th String Quartet, Beethoven’s Violin Concerto in D, and in Spohr’s Piano Quintet in D Major. I may also add that it is a highly common chord progression in barbershop.
This is really just the result of turning the minor common-tone diminished on its head. It is heard in a number of romantic period compositions such as the Moonlight Sonata. When you see the clear harmonic justification of the chords in that they trace a just flatted-9th chord, this suggests that the minor common diminished could be utonal, or sub-harmonic, in nature.
ii7 V7; iiø7 V7
This is a supertonic minor7th or half-diminished 7th to dominant 7th, often heard in barbershop. The use of a septimal minor and septendecimal half-diminished 7ths corrects an abrupt pitchbend in standard just tunings are used.
The 2nd variant is the one chord progression in the list with two tritone complements: The tritone complement of the second chord (dominant 7th) will give you the Muszourski Chords. The tritone complement of the first chord (half-diminished 7th) will give you the Tristan Half-Cadence. They're muscially different but enharmonically equal.
Tritone Complement: Muszourski chords, Tristan Half-Cadence
This has been heard in many nuances from the late classical into the jazz era. It is native to the jazz minor scale. It has an awe-inspiring appearance, though probably unnoticed by many listeners, in the 1812 Overture."
So-called because it is a cadence tuned to the Spanish scale (the 5th mode of the harmonic minor scale). This scale has a half-diminished 7th chord on the dominant and a major-minor 7th chord on the tonic, making for some of the must beautiful harmonies in the music of the Spanish and Latino traditions.
Inverse: One Two (minor)
The Tristan 6th chord. can be found as the 7th chord rooted on the 7th degree of the Hungarian-minor scale as a minor-diminished 7th chord, but works well in third inversion on the 6th degree. This peculiar augmented 6th chord is an enharmonic of the half-diminished 7th, but it has no commonly known name. I have called it the Neptune 6th after its use in the “Neptune” movement of Holst’s Planets. Lately I’ve been referring to it as the Tristan 6th chord, because analysis of the famous chord in Tristan and Isolde shows it spelled as an augmented 6th in the key of A minor. Wagner didn't fully resolve it, except as an indirect half-cadence to an E dominant 7th. Its most common use in the classical and romantic eras is as what I call a “tristan mordent”, where it is used briefly to embellish a German 6th chord by flatting the 3rd and 5th.
Inverse: German 6th Full Resolution
Tritone Complement: Inverse Cadence
The only examples I can think of that use this full resolution of the chord are as follows:
inverse: German to Tonic Tritone Complement: Spanish Cadence
This partial resolution of the Tristan consists of resolving the augmented 6th to an octave.
The minor variant can be called the “Franck’s Chords”, based on its copious use in Franck’s symphony and in his Le Chasseur maudit.
This is the resolution that is used (in a roundabout way) by the original “Tristan chord” in Wagner’s prelude. This is a Tristan 6th followed by the dominant 7th. Wagner does insert two French 6th chords in between these in the actual prelude. The tuning consists of a just Half-Diminished 7th followed by a Harmonic 7th with the 3rd fixed between them.
These two chords are enharmonic to the Muszourski Chords.
Inverse: Muszourski Chords
Tritone Complement: Minor Half-Cadence
Here is the most common use of this rather peculiar augmented 6th chord hidden in the Hungarian Minor scale and kind of overlooked. It is the result of taking the two interior notes of the German 6th (the 3rd and 5th) down a minor 2nd, resulting in another augmented 6th chord of the same Hungarian Minor scale, known as the Tristan 6th. This chord motion is commonly used even by Mozart and those of his period.
This fully resolves the chromatic intervals, the augmented 5th, the diminished 3rd, and the diminished 5th, of the augmented-minor 7th chord.
Probably the most well-known example of this pretty obscure chord change is the donkey ride section in the Grand Canyon Suite.
Also known as: Till 6th Resolution
This chord is named after it being the most prominent chord in Strauss's Till Eulenspiegel’s Merry Pranks. It is another enharmonic of the Half-diminished 7th chord, but this one has the tricky double-augmented 4th. It can be found in the Eulenspiegel scale which is the union of the notes in the Eulenspiegel 6th and its resolving tonic chord.
This fully resolves the chromatic intervals, the augmented 4th, the augmented 6th and the doubly-augmented 4th, in the Eulengpiegel 6th chord, and was the resolution used by Strauss.
Inverse: Swiss 6th Resolution
Tritone Complement: Leading Cadence
After the sweet sound of the diminished and the passionate sound of the German, you move into a more magical quality with this chord, rooted on the 2nd degree of the Hungarian-minor scale, but is often used in 2nd inversion as an augmented 6-4 chord on the 6th degree of the scale. It's name is of uncertain origin but may have been well-used by the likes of composers like Debussy and Ravel, or probably because the the idea of “frenchness” is denoted by the unrestrained color of the chord.
These are the two chords that are prominently used throughout the Al Parson's Project song Time.
Also known as: Cuckoo Chords
This has been termed the Belgian 6th chord by music scholar Mark DeVoto. This augmented 6th chord and its resolution to a 6/4 tonic is heard hauntingly in Franck’s Les Éolides. I have named them the “cuckoo chords” after their provocative use in Saint-Saens’s depiction of the cuckoo in his Carnival of the Animals. The chord pair can also be heard in the jazz world as the two opening chords of Take the A Train.
So named because this pair of chords are the two that stick tightly in your ears after hearing the “old castle” section of Pictures at an exhibition by Muszourski.
So named because this pair of chords was alternated in an ominously colorful way in Khachaturian's Adagio of Spartacus. It is essentially an Eulenspiegel 6th followed by its related dominant 7th. In the context of the adagio, it functions as a secondary dominant.
This bitter-sweet progression connects two major 7th chords with a French 6th. The first tuning puts the first two hangers on the 1st and 5th harmonics so they can both remain stationary. The french results from flatting the major 7th of the first chord to a harmonic 7th and flatting the 5th to an 11th. The other two tunings put the two hangers the 7th and 11th harmonics, which require at least one note to bend. Each tuning is based on which note is fixed. The resulting french results from a dominant 7th in the root position with the 5th on the top flatted to an 11th.
This three chord progression is often used in tags, as an excuse to use the colorful German 6th chord to connect two chords in a delightful way.
When the dominant 7th is substituted for the minor 7th in the third chord, the result is the “rose chords”, probably nicknamed after its use in Broadway Rose at the start of the chorus. Also look for it in the opening to One More Song.
I7 ♯iio7 iiø7 I
This commonly used progression is a dominant 7th chord and a half-diminished 7th chord connected by a diminished 7th chord. I named it after its use in Sweet Adeline, and it is also used in the tag of My Wild Irish Rose. The three moving parts form a just diminished triad that moves so that the hanging note is the root of the first chord, the 17th harmonic of the second chord, and the 9th of the third chord. The fourth chord closes it off with a simple triad.
♭III6/5 II7 ♭IIM7 I
I named this progression after its use in a popular TTBB version of the end of Lone Prairie. It can also be heard on Barbara Streisand's Evergreen. The three moving parts form a major triad that moves so that the the hanging note is the doubled root of the first chord, the major 7th of the 2nd chord, the septimal minor 7th of the third chord, and the major 6th of the 4th chord, Forming one of the most lovely progressions in gleeclub harmony.
I iiio7 V7
This progression is a favorite in barbershop harmony when you have a lead “hanger” in a tonic chord that moves to the dominant 7th chord, with a glorious diminished 7th chord connecting the two. The tuning I depict here in the major version is the diminished 7th that is tuned with the preceding triad as an inverse commontone diminished. A suitable alternative would be a tuning more in line with the following dominant 7th, based on the Barcarolle chords.
This is a common barbershop progression when there is a post on the 5th or 7th of a dominant chord. It can be heard in the tag of Hard Hearted Hanna and in the intro to Chordbuster March.
vi7 vio7 ii7
This sequence is a common one that sweetened the sound of the swing era: two minor 7th chords connected by a passing diminished 7th chord. I named the sequence after its use in Moonlight Serenade. I prefer the hanging 3rd tuning because in it the two inner notes form the just minor 3rd in the diminished 7th chord, allowing them both to remain stationary.
This is also a barbershop standard, an augmented chord shooting off from the barbershop seventh toward to which that augmented chord strongly tends.
Gleeclub composition: roots move in 5-limit progression, absent any ragtime progression ending in the tonic.
Barbershop composition: roots move in barbershop ragtime progression following Pythagorean roots.
Index of Intervals
Glossary of Just Intonation
Tables of Pitch Bends
Fun with Vowel Formants
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